The statistical design of medical experiments for evaluating new treatments in comparison with a control (which may be either a standard treatment or a placebo) is treated in a large and rapidly growing statistical methods literature. This literature is, however, largely disused in favor of methods 25 or more years old. This is due in large to serious deficiencies in the new statistical methods of the past 25 years, which render them unsuitable for medical application. The objective of this research is to develop a treatment vs. control statistical model which is sufficiently flexible to allow adaptation to, and provide useful methods for, accurate modern statistical design and analysis of human and animal tumor studies. The final model will include a convincing test of the null hypothesis, but not the hopeless-to-specify "patient horizon". Selection bias will be controlled by partial randomization. A two-stage model, formulated to capture the best of fixed-sample (one-stage) simplicity and sequential efficiency, will be emphasized. Heteroscedasticity (unequal unknown response variable variances) will be allowed for.